This The Mentalist screencap contains
snap brim hat, boater, leghorn, panama, panama hat, sailor, skimmer, straw hat, fedora, felt hat, homburg, stetson, and trilby.
There might also be
dress hat, high hat, opera hat, silk hat, stovepipe, top hat, topper, beaver, pith hat, pith helmet, sun helmet, topee, and topi.